Based on past experience, a bank believes that 7% of the people who receive loans will not make payments on time.The bank has recently approved 300 loans.What is the probability that over 8% of these clients will not make timely payments?
A)0.752
B)0.504
C)0.248
D)0.68
E)0.496

Question

Quizplus · Accepted Answer

This is a binomial probability problem that can be approximated using the normal distribution because the sample size is large (n = 300). The mean (μ) of the distribution of the proportion of clients not making timely payments is np = 300 * 0.07 = 21. The standard deviation (σ) is sqrt(np(1-p)) = sqrt(300*0.07*0.93) ≈ 4.34. To find the probability of more than 8% (which is 24 out of 300) not making timely payments, we convert 24 to a z-score: z = (24 - 21) / 4.34 ≈ 0.69. Looking up 0.69 on the z-table gives a left-tail probability, so we subtract this from 1 to find the upper tail probability, which is approximately 0.248.

Based on Past Experience, a Bank Believes That 7% of the People